CONNECTION OF CIRIC TYPE F-CONTRACTION INVOLVING FIXED POINT ON CLOSED BALL

Abstract

This paper is a continuation of the investigations of F-contractions. The aim of this article is to extend the concept of Ćirić type F-contraction in closed ball. We introduce the notion of F-contraction on closed ball and introduced new approach of fixed point theorems for F-contraction on closed ball in a complete metric space. Our results is very useful for the contraction of the mapping only on closed ball instead on the whole space. Some comparative examples are constructed which illustrate the superiority of our results. Our results provide extension as well as substantial generalizations and improvements of several well known results in the existing comparable literature.

Keywords

• Metric space,fixed point; F contraction; Closed ball.

References

1. M. Abbas, B. Ali and S. Romaguera, Fixed and periodic points of generalized contractions in metric spaces, Fixed Point Theory Appl. 2013, 2013:243.
2. --------------------------------------------------------------------------
3. T. Abdeljawad, Meir-Keeler contractive xed and common xed point theorems, Fixed PoinTheory Appl. 2013 doi:10.1186/1687-1812-2013-19.
4. --------------------------------------------------------------------------[3] . Acar and I. Altun, A Fixed Point Theorem for Multivalued Mappings with -Distance, Abstr. Appl. Anal., Volume 2014, Article ID 497092, 5 pages.
5. ------------------------------------------------------------------------[4] M. Arshad , Fahimuddin, A. Shoaib and A. Hussain, Fixed point results for - -locally graphic contraction in dislocated qusai metric spaces, Math Sci., (2014) doi 10.1007/s40096-014-0132, 7 pages.
6. ---------------------------------------------------------------------
7. M. Arshad , A. Shoaib, I. Beg, Fixed point of a pair of contractive dominated mappings on a closed ball in an ordered complete dislocated metric space, Fixed Point Theory and Appl. (2013), 2013:115, 15 pp.
8. ----------------------------------------------------------------------

9. M. Arshad, A. Shoaib, and P. Vetro, Common Fixed Points Of A Pair Of Hardy Rogers Type Mappings On A Closed Ball In Ordered Dislocated Metric Spaces, Journal of Function Spaces and Appl. 2013 (2013), article ID 638181, 9 pages.
10. ----------------------------------------------------------------------
11. A. Azam, S. Hussain and M. Arshad, Common fixed points of Chatterjea type fuzzy mappings on closed balls, Neural Computing & Applications, (2012) 21 (Suppl 1):S313S317.
12. --------------------------------------------------------------------
13. A. Azam, M. Waseem, M. Rashid, Fixed point theorems for fuzzy contractive mappings in quasi-pseudo-metric spaces, Fixed Point Theory Appl., 20132013:27.
14. --------------------------------------------------------------------
15. S.Banach, Sur les opØrations dans les ensembles abstraits et leur application aux equations itegrales, Fund. Math., 3 (1922) 133181.
16. ------------------------------------------------------------------
17. Lj.B. Circ, Generalized contractions and fixed point theorems, Publ. Inst. Math., 12 (26) (1971), 1926.
18. -------------------------------------------------------------------
19. LB. ·Ciri·c, A generalization of Banachs contraction principle. Proc. Am. Math. Soc., 45 (1974) 267-273.
20. --------------------------------------------------------------------
21. M. Cosentino, P. Vetro, Fixed point results for F-contractive mappings of Hardy-Rogers-Type, Filomat 28:4(2014), 715-722. doi:10.2298/FIL1404715C
22. ---------------------------------------------------------------------
23. M. Edelstein, On xed and periodic points under contractive mappings. J. Lond. Math. Soc., 37, 74-79 (1962).
24. --------------------------------------------------------------------
25. B. Fisher, Set-valued mappings on metric spaces, Fundamenta Mathematicae, 112 (2) (1981) 141145.
26. ---------------------------------------------------------------------
27. M. Geraghty, On contractive mappings, Proc. Amer. Math. Soc., 40 (1973) 604-608.
28. ---------------------------------------------------------------------
29. N. Hussain, M. Arshad, A. Shoaib and Fahimuddin, Common xed point results for -contractions on a metric space endowed with graph, J. Inequal. Appl., (2014) 2014:136.
30. ---------------------------------------------------------------------
31. N. Hussain and P. Salimi, suzuki-wardowski type xed point theorems for -GF-contractions, Taiwanese J. Math., 20 (20) (2014), doi: 10.11650/tjm.18.2014.4462
32. -----------------------------------------------------------------------
33. N. Hussain, E. Karap‹nar, P. Salimi and F. Akbar, -admissible mappings and related xed point theorems, J. Inequal. Appl., 114 (2013) 1-11.
34. --------------------------------------------------------------------
35. N. Hussain, P Salimi and A. Latif, Fixed point results for single and set-valued -- -contractive mappings, Fixed Point Theory Appl. 2013, 2013:212.
36. --------------------------------------------------------------------
37. N. Hussain, E. Karapinar, P. Salimi, P. Vetro, Fixed point results for GmMeir-Keeler contractive and G-(; )-Meir-Keeler contractive mappings, Fixed Point Theory Appl. 2013, 2013:34. ----------------------------------------------------------------------
38. N. Hussain, S. Al-Mezel and P. Salimi, Fixed points for Alpha-Psi -graphic contractions with application to integral equations, Abstr. Appl. Anal., (2013) Article 575869.
39. ---------------------------------------------------------------------
40. E. Karapinar and B. Samet, Generalized ( Alpha, psi) contractive type mappings and related xed point theorems with applications, Abstr. Appl. Anal., (2012) Article id:793486.
41. -----------------------------------------------------------------------[23] E. Kryeyszig., Introductory Functional Analysis with Applications, John Wiley & Sons, New York, (Wiley Classics Library Edition) 1989.
42. -----------------------------------------------------------------
43. MA. Kutbi, M. Arshad and A. Hussain, On Modied Contractive mappings, Abstr. Appl. Anal., (2014) Article ID 657858, 7 pages.
44. -----------------------------------------------------------------------
45. G. Minak, A. Halvaci and I. Altun, ·Ciri·c type generalized Fcontractions on complete metric spaces and xed point results, Filomat, 28 (6) (2014), 1143-1151.
46. -----------------------------------------------------------------------
47. SB. Nadler, Multivalued contraction mappings, Pac. J. Math., 30 (1969), 475-488.
48. ----------------------------------------------------------------------
49. H. Piri and P. Kumam, Some xed point theorems concerning Fcontraction in complete metric spaces, Fixed Poin Theory Appl. (2014) 2014:210.
50. ----------------------------------------------------------------------
51. M. Sgroi and C. Vetro, Multi-valued F-contractions and the solution of certain functional and integral equations, Filomat 27:7 (2013), 12591268.
52. ---------------------------------------------------------------------
53. P. Salimi, A. Latif and N. Hussain, Modied -Contractive mappings with applications, Fixed Point Theory Appl. (2013) 2013:151.
54. ------------------------------------------------------------------------
55. NA. Secelean, Iterated function systems consisting of F-contractions, Fixed Point Theory Appl. 2013, Article ID 277 (2013). doi:10.1186/1687-18122013-277.
56. ------------------------------------------------------------------------
57. M. Sgroi, C. Vetro, Multi-valued FContractions and the Solution of certain Functional and integral Equations, Filomat 27:7, (2013), 1259-1268.
58. ----------------------------------------------------------------------
59. A. Shoaib, M. Arshad and J. Ahmad, Fixed point results of locally cotractive mappings in ordered quasi-partial metric spaces, The Scientic World Journal, 2013 (2013), Article ID 194897, 8 pp.
60. -----------------------------------------------------------------------
61. B. Samet, C. Vetro and P. Vetro, Fixed point theorems for -contractive type mappings, Nonlinear Anal. 75 (2012) 21542165.
62. ------------------------------------------------------------------------[34] D. Wardowski, Fixed point theory of a new type of contractive mappings in complete metric spaces. Fixed PoinTheory Appl. (2012) Article ID 94.
63. ------------------------------------------------------------------------